AWhat changed
A randomly shifted geometric dissection has a near-optimal Euclidean tour with few boundary crossings; portal-based dynamic programming gives an approximation scheme in any fixed dimension.
Scientific scope
A randomly shifted geometric dissection has a near-optimal Euclidean tour with few boundary crossings; portal-based dynamic programming gives an approximation scheme in any fixed dimension. The approximation scheme concerns Euclidean TSP in fixed dimension with fixed requested accuracy. Its randomized structural theorem succeeds with a stated probability over shifts, not for every shift. Portals, crossing bounds, preprocessing and rounding have costs; the method is neither an exact solver nor a uniform efficient scheme in dimension/accuracy. General metric TSP and later practical improvements are separate. Theoretical parallelism is not a measured hardware speedup.
Evidence
Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.
Contributors
- Sanjeev Arora · SCIENCE: Original completebyline scientific author; no claim ownership of antecedents or independent Mitchell work.
- Joseph Mitchell · SCIENCE: Source-reported independent planar PTAS; distinct contribution not this paper coauthorship.
- Karen Wang; Warren Smith; Michel Goemans · PARTICIPATION: Source-acknowledged counterexample exploration andportal suggestions; no invented byline or effortfractions.
Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.
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